
	Where results make sense

Topic: Tale cohomology

	Cohomology - Wikipedia, the free encyclopedia
		That is, cohomology is defined as the abstract study of cochains, cocycles and coboundaries.
		Cohomology can be viewed as a method of assigning algebraic invariants to a topological space that has a more refined algebraic structure than does homology.
		Cohomology arises from the algebraic dualization of the construction of homology.
	en.wikipedia.org /wiki/Cohomology (679 words)

	Motive (algebraic geometry) - Wikipedia, the free encyclopedia
		Mathematically, the theory of motives is then the conjectural "universal" cohomology theory for such objects.
		This information is already given by the Weil conjectures (which are now proven), and the standard conjectures are part of the effort to extend these results to characteristic 0.
		Possible adequate equivalences are given by rational equivalence, algebraic equivalence, and homological equivalence, and numerical equivalence on cycles.
	en.wikipedia.org /wiki/Motive_%28mathematics%29 (963 words)

	PlanetMath: sheaf cohomology
		Sheaf cohomology can be explicitly calculated using Čech cohomology.
		In fact in [2], this is how the cohomology of projective space is explicitly calculated.
		This is version 10 of sheaf cohomology, born on 2003-08-14, modified 2005-05-15.
	www.planetmath.org /encyclopedia/SheafCohomology.html (219 words)

	Étale cohomology - Slider
		In mathematics, the étale cohomology theory of algebraic geometry is a refined construction of homological algebra, introduced in order to attack the Weil conjectures.
		The formal definition of étale cohomology is as the derived functor of the functor of sections,
		The étale requirement is the condition that would allow one to apply the implicit function theorem if it were true in algebraic geometry (but it isn't – implicit algebraic functions are called algebroid in older literature).
	enc.slider.com /Enc/L-adic_cohomology (961 words)

	Alexander Grothendieck - Wikipedia, the free encyclopedia
		Perhaps Grothendieck's deepest single accomplishment is the invention of the étale and l-adic cohomology theories, which explain an observation of André Weil's, that there is a deep connection between the topological characteristics of a variety and its diophantine (number theoretic) properties.
		Weil realized that to prove such a connection one needed a new cohomology theory, but neither he nor any other expert saw how to do this until such a theory was found by Grothendieck.
		Crystals and crystalline cohomology, yoga of De Rham and Hodge coefficients.
	en.wikipedia.org /wiki/Alexander_Grothendieck (1595 words)

	[No title]
		It is a subgroup of the Galois cohomology group $H^{n}(K,\z)$ (abbreviated to $H^{n}(K)$) and is defined as \begin{equation*}H^{n}_{nr}(K/k) = \underset {{v \in {\mathcal{V}}(K)} }{\bigcap }H^{n}_{\acute e t}(Spec~{\mathcal{O}}_{v}, \mu _{2}).
		Unramified cohomology and \'{e}tale cohomology} In this section, we use the results of Szyjewski and compute the structure of the unramified cohomology group $\unrkc {3}$.
		The middle exact row is the long exact cohomology sequence associated to a quadratic extension of the ground field.
	www.ams.org /tran/1997-349-06/S0002-9947-97-01940-5/S0002-9947-97-01940-5.tex (8319 words)

	Sleeping Beauty (Site not responding. Last check: 2007-10-07)
		Sleeping Beauty ("La Belle aux bois dormant") is a fairy tale classic the in the set published in 1697 by Charles Perrault Contes de ma Mere l'Oye ("Mother Goose Tales").
		Perrault so transformed the tale of a beauty "Sole Luna e Talia" in Giambattista collection of tales Il Pentamerone that she is scarcely recognizable in first part of the tale the only that is still current.
		Perrault's is an aristocratic tale told a high-bourgeois audience inculcating female patience and There are earlier elements that contributed to tale in the medieval courtly romance Perceforest (published in 1528) in which a named Zellandine falls into an enchanted sleep is raped by a wandering prince resulting the birth of their child.
	www.freeglossary.com /Sleeping_Beauty (1702 words)

	PlanetMath: small site on a scheme
		Since an étale morphism is open, one can view them as open subsets with a ``twisted'' embedding.
		This nontrivial embedding yields new behaviour from sheaves and presheaves, and the cohomology
		This is version 4 of small site on a scheme, born on 2004-02-10, modified 2005-10-18.
	www.planetmath.org /encyclopedia/SmallSiteOnAScheme.html (232 words)

	Jean-Pierre_Serre (Site not responding. Last check: 2007-10-07)
		In simple terms, the cohomology of a coherent sheaf over a finite field couldn't capture as much topology as singular cohomology, with integer coefficients.
		This was one important step towards the eventual ''�tale covering'' theory.
		Amongst his most original contributions were: the concept of algebraic K-theory; the Galois representation theory for l-adic cohomology and the conceptions that these representations were 'large'; and the Serre conjecture on mod p representations that made Fermat's last theorem a connected part of mainstream arithmetic geometry.
	goc.subdomain.de /Jean-Pierre_Serre (533 words)

	Arithmetic Duality Theorems:0124980406:Milne, J.S.:eCampus.com
		Here, published for the first time, are the complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry.
		The text covers these theorems in Galois cohomology, tale cohomology, and flat cohomology and addresses applications in the above areas.
		The writing is expository and the book will serve as an invaluable reference text as well as an excellent introduction to the subject.
	www.ecampus.com /bk_detail.asp?isbn=0124980406 (74 words)

	Geometry-Algebra-Singularities-Combinatorics Seminar Talk (Site not responding. Last check: 2007-10-07)
		Abstract: Classical (oriented) cobordism is a generalized cohomology theory for topological spaces, in fact the universal cohomology theory which posses a projective bundle formula.
		As such, it maps to the more familiar theories of singular cohomology and topological K-theory.
		Together with Fabien Morel, I have developed a version of cobordism in algebraic geometry, which has the relation to topological cobordism that algebraic K_0 has to topological K-theory, and that the Chow ring has to singular cohomology.
	www.math.neu.edu /GASC/GAS/levine.html (122 words)

	Pure Group Publications
		Finally Voevodsky (c.1997) devised an entirely new construction of motivic cohomology which enabled him to determine the $2$-adic part of the K-theory of any field admitting the resolution of singularities.
		Voevodsky's work establishes (at the prime $p=2$) the 1973 conjecture of Quillen and Lichtenbaum, which relates K-theory with mod $p^{n}$ coefficients to Grothendieck's \'{e}tale cohomology with mod $p^{n}$ coefficients.
		Incidentally, Snaith and his collaborators proved the surjectivity half of the Quillen-Lichtenbaum conjecture for general smooth, projective schemes (Inventiones 1982).
	www.maths.soton.ac.uk /pure/researchabstract.phtml?keyword=K-theory (422 words)

	Amazon.de: Bücher: Real and Etale Cohomology. (Site not responding. Last check: 2007-10-07)
		This book makes a systematic study of the relations between the étale cohomology of a scheme and the orderings of its residue fields.
		A major result is that in high degrees, étale cohomology is cohomology of the real spectrum.
		It is of interest to graduate students and researchers who work in algebraic geometry (not only real) and have some familiarity with the basics of étale cohomology and Grothendieck sites.
	www.amazon.de /exec/obidos/ASIN/3540584366 (378 words)

	[No title]
		That algorithm exploits divisors on the curve instead of points on an abelian variety, number fields instead of cohomology groups and functions on the curve instead of coboundary maps.
		Up until now, Selmer groups have been computed in the cases that the image of the isogeny is a Jacobian (using Galois cohomology) or the abelian varieties are modular (using \'{e}tale cohomology).
		In order to replace computations in cohomology groups with computations in number fields, one must work in the \'{e}tale algebra corresponding to (a subset of) the kernel of the dual of the given isogeny.
	math.scu.edu /~eschaefe/jnt.tex (6349 words)

	On 2-adic cyclotomic elements in K-theory and étale cohomology of the ring of integers (ResearchIndex)
		On 2-adic cyclotomic elements in K-theory and étale cohomology of the ring of integers (ResearchIndex)
		On 2-adic cyclotomic elements in K-theory and étale cohomology of the ring of integers
		Abstract: In this paper we define 2-adic cyclotomic elements in K-theory and andEacute;tale cohomology of the integers.
	citeseer.ist.psu.edu /24204.html (323 words)

	Deligne Cohomology for Orbifolds, Discrete Torsion and B-Fields (ResearchIndex) (Site not responding. Last check: 2007-10-07)
		We prove that the third Deligne cohomology group H D) of a smooth andEacute;tale groupoid classify gerbes with connection over the groupoid.
		We argue that the B-field and the discrete torsion in type II superstring theories are special kinds of gerbes with connection, and finally, for each one of them, using Deligne cohomology we construct a at line bundle over the inertia groupoid, namely a Ruan inner local system in...
		1 Deligne cohomology of etale groupoids (context) - Lupercio, Uribe
	sherry.ifi.unizh.ch /lupercio02deligne.html (339 words)

	Rational Isomorphisms Between (ResearchIndex)
		Abstract: The well known isomorphism relating the rational algebraic K-theory groups and the rational motivic cohomology groups of a smooth variety over a field of characteristic 0 is shown to be realized by a map (the "Segre map") of infinite loop spaces.
		0.2: Infinitesimal 1-Parameter Subgroups And Cohomology - Suslin, Friedlander, Bendel (1997)
		Weight Zero Motivic Cohomology and the General Linear Group of a..
	citeseer.ist.psu.edu /616849.html (734 words)

	Abstract 1229 (Site not responding. Last check: 2007-10-07)
		In this paper we introduce the concept of Deligne cohomology of an orbifold.
		We prove that the third Deligne cohomology group $H^3(\Gg,\integer(3)_D^\infty)$ of a smooth \'{e}tale groupoid classify gerbes with connection over the groupoid.
		We argue that the $B$-field and the discrete torsion in type II superstring theories are special kinds of gerbes with connection, and finally, for each one of them, using Deligne cohomology we construct a flat line bundle over the inertia groupoid, namely a Ruan inner local system\cite{Ruan} in the case of an orbifold.
	www.esi.ac.at /Abstracts/abs1229.html (95 words)

	[No title]
		Note that this implies that the de Rham cohomology of $X$ depends only on its reduction mod $p$ and that it inherits a Frobenius action from $H^i_{cris}(X_0/S)$.
		Then the de Rham cohomology $H^4_{DR}(X/S)$ is torsion free with Hodge numbers: \begin{align} & h^{0,4}=h^{4,0}=0 \\ &h^{1,3}=h^{3,1}=1 \\ & h^{2,2}=21 \end{align} Furthermore, the Hodge to de Rham spectral sequence degenerates at $E_1$.
		When this functor is applied to the \'etale cohomology of an algebraic variety $Y$ over $K$ with good reduction, its output is the de Rham cohomology of $Y$ with the induced Frobenius action.
	www.math.ufl.edu /%7Elevin/tateconj.tex (5177 words)

	Princeton University Press Books in Mathematics
		Cohomology of Quotients in Symplectic and Algebraic Geometry.
		The Geometry and Cohomology of Some Simple Shimura Varieties.
		An Imaginary Tale: The Story of i [the square root of minus one].
	pup.princeton.edu /catalogs/subjects/math.html (1782 words)

	Citebase - Vertex algebras
		28-1 Therefore the infinitesimal deformations of the algebra V are classified by the cohomology group H 2 (V, V) of the asso ciative algebra V with co efficients in the 2-sided mo dule V.
		The G-equivariant cohomology groups are calculated (and defined) by replacing the (standard) co chains above by the G-invariant co chains.
		We first note that most definitions in group cohomology (in particular the homogeneous and inhomogeneous standard complexes) can easily be extended to the case of arbitrary co commutative Hopf algebras.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:q-alg/9706008 (5525 words)

	Motivic cohomology and algebraic cycles a categorical approach, by Marc Levine
		For S a field of characteristic zero, or a smooth curve over a field of characteristic zero, the motivic cohomology agrees with Bloch's higher Chow groups; the same is true in characteristic p>0 if one uses Q-coefficients.
		In particular, the motivic cohomology agrees rationally with the weight-graded pieces of algebraic K-theory, for S smooth and of dimension at most one over a field.
		In addition, each reasonable graded cohomology theory Gamma(*) on the category of smooth, quasi-projective schemes over a fixed base S gives rise to a realization functor Re_Gamma for DM(S); for example, we have the Betti, e'tale and Hodge realizations of DM(S).
	www.math.uiuc.edu /K-theory/0107/index.html (202 words)

	[No title]
		} \date{July 11, 1993} \keywords{Algebraic geometry, \'{e}tale cohomology, $p$-adic analytic spaces} \maketitle \section*{Introduction } In this work we develop a formalism of vanishing cycles for non-Archimedean analytic spaces which is an analog of that for complex analytic spaces from \cite{SGA7}, Exp. XIV.
		Like \cite{Ber3}, this work arose from a suggestion of P. Deligne to apply the \'{e}tale cohomology theory from \cite{Ber2} to the study of the vanishing cycles sheaves of schemes.
		Artin, A. Grothendieck, and J.-L. Verdier, {\em Th\'{e}orie des Topos et Cohomologie \'{E}tale des Sch\'{e}mas}, Lecture Notes in Math.
	www.ams.org /jams/1996-9-04/S0894-0347-96-00214-7/S0894-0347-96-00214-7.tex (7228 words)

	Notes * Loving Reminders for Couples 60... (Site not responding. Last check: 2007-10-07)
		Monarch Notes on Dickens a Tale of Two Cities.
		Dickens A Tale of Two Cities Cliffs Notes.
		Cohomology of Quotients in Symplectic and Algebraic Geometry Mathematical Notes, 31.
	www.searchthebook.net /?sear_search=Notes (1800 words)

	Books on John Roe (Site not responding. Last check: 2007-10-07)
		The theory is then used to construct "higher indices" for elliptic operators on noncompact complete Riemannian manifolds.
		Such an elliptic operator has an index in the $K$-theory of a certain operator algebra naturally associated to the coarse structure, and this $K$-theory then pairs with the coarse cohomology.
		It's a tale that has been recounted many times but now for the first time appears in print, complete with illustrations by the author's son, Peter, a classical animator at Nelvana.
	books.bankhacker.com /John+Roe (1024 words)

	Professor Kostant's Homepage (Site not responding. Last check: 2007-10-07)
		A Theorem of Frobenius, A Theorem of Amitsur-Levitski and Cohomology Theory, J. of Math.
		Lie Algebra Cohomology and the Generalized Borel-Weil Theorem, Ann.
		Quantum Cohomology of the Flag Manifold as an Algebra of Rational Functions on a Unipotent Algebraic Group, Deformation Theory and Symplectic Geometry, Edited by D. Sternheimer et al, Kluwer, (1997), 157-175.
	www-math.mit.edu /~kostant (1337 words)

	[No title]
		There is an increasing filtration on $\hcris$, the crystalline cohomology of $\xo$, given by $F^i_{conj}\hcris =$ the largest subcrystal with slopes less than or equal to $i$.
		This fact can be used to show that the Frobenius map actually acts on on the {\it rational} cohomology $H^4(X_{\Bbb C}, \Bbb Q)$ in a manner which is compatible with its action on \'{e}tale cohomology.
		Let $\primhz$ be its primitive cohomology and let $q$ be the nondegenerate quadratic form induced by cup product.
	www.math.ufl.edu /%7Elevin/thesis.tex (7819 words)

	The Theory of the Leisure Class (Site not responding. Last check: 2007-10-07)
		Gintis, Herbert Full-text papers and class material covering game theory, the rational actor model in economic theory, experimental economics and anthropology.
		Home Page of J. Milne Includes preprints and course notes on Group Theory, Fields and Galois Theory, Algebraic Geometry, Algebraic Number Theory,Modular Functions and Modular Forms, Elliptic Curves, Abelian Varieties, Etale Cohomology, and Class Field Theory.
		Veblen: The Theory of the Leisure Class: Cover The first and still foremost of the modern attack on wealth.
	www.serebella.com /encyclopedia/article-The_Theory_of_the_Leisure_Class.html (419 words)

	HogBlog: Mathematics Archives
		I used that to translate de Rham cohomology into the cohomology of the Lie algebra, and, upon translation, found that the Hodge decomposition gave a completely natural and completely representation-theoretic description of both Lie derivatives and the cohomology spaces: the cohomology spaces turned out to be the submodules of invariants in the cochain spaces.
		So de Rham cohomology on a compact Lie group is really a special case of the representation theory of Lie algebras.
		Here's someone's thesis, which is mainly on cohomology of restricted Lie algebras, but has a section on the more standard case as well.
	www.koschei.net /blog/archives/cat_mathematics.html (11621 words)

Try your search on: Qwika (all wikis)